3-loop diagrams of the ladder-type, which emerge for local quarkonic twist-2 operator matrix elements, are computed directly for general values of the Mellin variable N using Appell-function representations and applying modern summation technologies provided by the package Sigma and the method of hyperlogarithms. In some of the diagrams generalized harmonic sums with ξ ∈ {1, 1/2, 2} emerge beyond the usual nested harmonic sums. As the asymptotic representation of the corresponding integrals shows, the generalized sums conspire giving well behaved expressions for large values of N . These diagrams contribute to the 3-loop heavy flavor Wilson coefficients of the structure functions in deep-inelastic scattering in the region Q 2 ≫ m 2 .

The O(α 3 s n f T 2 F C A,F ) terms to the massive gluonic operator matrix elements are calculated for general values of the Mellin variable N . These twist-2 matrix elements occur as transition functions in the variable flavor number scheme at NNLO. The calculation uses sum-representations in generalized hypergeometric series turning into harmonic sums. The analytic continuation to complex values of N is provided.

Starting at 3-loop order, the massive Wilson coefficients for deep-inelastic scattering and the massive operator matrix elements describing the variable flavor number scheme receive contributions of Feynman diagrams carrying quark lines with two different masses. In the case of the charm and bottom quarks, the usual decoupling of one heavy mass at a time no longer holds, since the ratio of the respective masses, η = m 2 c /m 2 b ∼ 1/10, is not small enough. Therefore, the usual variable flavor number scheme (VFNS) has to be generalized. The renormalization procedure in the two-mass case is different from the single mass case derived in [1]. We present the moments N = 2, 4 and 6 for all contributing operator matrix elements, expanding in the ratio η. We calculate the analytic results for general values of the Mellin variable N in the flavor non-singlet case, as well as for transversity and the matrix element A(3) gq . We also calculate the two-mass scalar integrals of all topologies contributing to the gluonic operator matrix element A gg . As it turns out, the expansion in η is usually inapplicable for general values of N . We therefore derive the result for general values of the mass ratio. From the single pole terms we derive, now in a two-mass calculation, the corresponding contributions to the 3-loop anomalous dimensions. We introduce a new general class of iterated integrals and study their relations and present special values. The corresponding functions are implemented in computer-algebraic form.(2),NS qq,Q (N F + 2) δ 2 +Ĉ(2),NS q,(2,L) (N F ) 5 The sum in Eq. (2.19) is over the words w given by the different orderings of the Lorentz indices. For example, for M = 3 one obtains, Sf µ1,µ2,µ3 = 1 6 (f µ1,µ2,µ3 + f µ1,µ3,µ2 + f µ2,µ1,µ3 + f µ2,µ3,µ1 + f µ3,µ1,µ2 + f µ3,µ2,µ1 ).

We compute the contribution to the total cross section for the inclusive production of a Standard Model Higgs boson induced by two quarks with different flavour in the initial state. Our calculation is exact in the Higgs boson mass and the partonic center-of-mass energy. We describe the reduction to master integrals, the construction of a canonical basis, and the solution of the corresponding differential equations. Our analytic result contains both Harmonic Polylogarithms and iterated integrals with additional letters in the alphabet.

Abstract:We compute next-to-leading order QCD corrections to the process gg → ZH. In the effective-theory approach we confirm the results in the literature. We consider top quark mass corrections via an asymptotic expansion and show that there is a good convergence below the top quark threshold which describes approximately a quarter of the total cross section. Our corrections are implemented in the publicly available C++ program ggzh.